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<a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
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First@ RealDigits[N[3/4/Pi, 120]] (* Michael De Vlieger, Mar 15 2016 *)
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Consider generic prisms with triangular bases (tp) which can be fit inside , enclosed by a sphere, and let f(tp) be the fraction of the sphere volume occupied by any of them (i.e., the ratio of the prism volume to the sphere volume). Then this constant is the supremum of f(tp). It is attained by prisms which have as their base equilateral triangles with edge lengths r*sqrt(2), and rectangular side faces that are r*sqrt(2) wide and r*2/sqrt(3) high, where r is the radius of the enclosing, circumscribed sphere.
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Consider generic prisms with triangular bases (tp) which can be fit inside a sphere, and let f(tp) be the fraction of the sphere volume occupied by any of them (i.e., the ratio of the prism volume to the sphere volume). Then this constant is the supremum of f(tp). It is attained by prisms which have as their base equilateral triangles with edge lengths r*sqrt(2), and rectangular side faces that are r*sqrt(2) wide and r*2/sqrt(3) high, where r is the radius of the enclosing , circumscribed sphere.
A Examples of similar constant, but constants obtained for cylinders other shapes enclosed in by spheres, is are: A020760 for cylinders and A165952 for cuboids.
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